For obvious reasons we tend to think of ‘optical’ systems as being relevant only at visible and near-visible wavelengths. In practice, however, we can use optical and free space beam methods over a much wider range — from below 50 GHz to the soft X-ray region. As a result, signals over most of the “mm-wave, terahertz, and infrared” region can be processed using instruments which employ optical beams in the same way as we might use metal wires or waveguides at lower frequencies. In general we wish practical systems to be as compact as possible without compromising the performance. The beams used therefore can't have an enormous cross-sectional width compared with the wavelength. This means that techniques based on Gaussian Beam Mode analysis are often the most appropriate to take diffraction effects into account. Compact systems of this type are often called Quasi-Optical to indicate that their basic elements are ‘optical’, but a beam mode approach is used to take the effects of finite wavelength into account.

Free space beams are a convenient, low loss, low dispersion way to carry many EM signals from place to place. However, many signal sources and detectors (or mixers) are very small. As a result, it is often most convenient to mount the source/detector in or on a waveguide and us an antenna to link or couple the guide mode into free space.


A particular advantage of using a length of guide between a device and free space is that we can use the guide to control the field pattern coupled onto or from the device. Ideally, the use of a single mode guide ensures that we can precisely define the radiated/received field. Figures 11.1 a and b show two examples. In fig 11.1a the output from a coherent source emerges along a graded index dielectric fibre guide. The fibre carries a Gaussian Mode whose size is maintained constant as the field propagates along the fibre. This emerges at the ‘cut end’ of the fibre (in practice an anti-reflection coating would be required). The fibre guided wave has a plane phasefront everywhere along the fibre. Hence the emerging free space Gaussian beam has its waist plane located at the end of the fibre. The waist size of the free space mode is then equal to the size of the mode which is transmitted along the fibre-guide. (The waist of a free space beam is always the place where the beam width is finite and the phasefront is ‘flat’ — i.e. the phasefront radius of curvature is infinite.) An arrangement like this forms the basis of many visible/near-visible devices.


Figure 11.1b shows the equivalent arrangement for frequencies in the microwave, mm-wave, and THz spectral region when standard rectangular guide is used. Unlike fibre guide, a rectangular metallic guide normally has a cross-sectional dimensions smaller than the free space wavelength of the radiation. Hence a simple open waveguide end tends (as we found in an earlier lecture) to radiate in all directions rather than producing a convenient beam. This problem can be overcome by using a suitable feed horn. Simple rectangular or pyramidal horns were mentioned in an earlier section. However, when a Gaussian beam is require a better form of feed horn is available. This is a conical corrugated feed (sometimes also called a Scalar Feed).



The scalar feed differs from the pyramidal horn in two ways. Firstly it has a circular cross section and aperture (the ‘base’ opening). Secondly, its inner surface is corrugated with a concentric, coaxial series of grooves. These groove are placed close together and are a quarter-wavelength deep. These changes alter the field pattern as it passes through the horn. As a result, the corrugated feed couples the standard fundamental waveguide mode into a free space pattern which is close to being a fundamental Gaussian beam. Although not perfect, a good feed of this type produces an beam which can couple around 95% of the field's power into/out of the fundamental Gaussian mode. Hence for most purposes this kind of feed can be used as a guide to free space beam single-mode transformer.


A detailed analysis of this type of conical feed reveals that the field at its aperture has a spherical phasefront whose center is at the apex of the cone. We can work out the phasefront radius of curvature and beamsize at the aperture of the feed from knowing the feed geometry. Given these two properties and knowing the radiation wavelength defines the free space beam it produces (or will receive efficiently).




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University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.